Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673153 | Indagationes Mathematicae | 2013 | 12 Pages |
Abstract
Let (Ω,Σ,μ) be a finite complete measure space and (X,ââ
âX) be a Banach space with the Banach dual Xâ. Let Lâ(μ,X) denote the space of all μ-measurable functions f:ΩâX such that esssupÏâΩâf(Ï)âX<â. We study the problem of the integral representation of some natural classes of linear operators from Lâ(μ,X) to a Banach space with respect to the corresponding operator measures. We characterize relatively Ï(bvcaμ(Σ,Xâ),Lâ(μ,X))-sequentially compact sets in the space bvcaμ(Σ,Xâ) of all countably additive measures ν:ΣâXâ of bounded variation with ν(A)=0 if μ(A)=0.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Marian Nowak,